Annual and monthly geometric mean return

CFA Level I
#1

Hi,

have read the following statistics in the curriculum:

Geometric mean returns:

S&P 500 annual = 9.84%

S&P 500 monthly = 0.79%.

Why (1+annual return) here does not equal (1 + monthly return) raised to the 12th power? A bit confused.

#2

where in the curriculum did you see this?

#3

reading 7, par. 7.4

#4

rounding…

1.0984^(1/12) = 1.00785 --> rounded up to 0.79%

#5

Thanks! now i see… absolutely right, annual returns should’ve been converted to monthly, not the other way around)

#6

It can be converted both ways, its just that the monthly return was rounded off.

#7

I did not say it cannot be converted both ways. Yes, you can, but once you try to do monthly-annual, instead of annual-monthly, you will face the problem posted in this topic. You will not obtain the precise figure stated in the curriculum.